Kerry sells hand-painted stoneware mugs online. She buys mugs from a supplier for $10 each. The lead time for the mugs to be delivered to Kerry is 3 days. The order cost is $100 per order, and the holding cost is $3 per mug per month. The demand for the hand-painted mugs can be modeled as a normally distributed random variable with a mean of 20 mugs/day and a standard deviation of 8 mugs/day. Assume 30 days per month, and each day is independent and identically distributed.

Kerry's hand-painted mugs are starting to become popular, and there are already blog posts and reviews on her mugs with quality paintings. If she runs out of mugs, she believes the loss in goodwill is effectively $20 per backorder.

What is the EOQ?

What should be the re-order point, R?

What is the expected inventory, E(I)?

Calculate the sum of the monthly purchase cost, ordering cost, and holding cost.